Finite Group Databasebeta

← C2×#14539335 #17903979

Subgroups — C2×#14539335 #17903979

Order 4352.

1902 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763364C211yesmaximal, characteristic
2C2×#125×D17C211yesmaximal, characteristic
3#14539335C2116yesmaximal, direct product factor
4C2×#11763219C211yesmaximal, characteristic, complemented
5C2×#11763218C211yesmaximal, characteristic, complemented
6C2×#11763215C211yesmaximal, characteristic, complemented
7C2×#11763210C212yesmaximal, complemented
8C2×#11763209C212yesmaximal, complemented
9C2×#11762850C212yesmaximal
10C2×#11762848C212yesmaximal
11C2×#11762761C211yesmaximal, characteristic
12C2×C17×#501C211yesmaximal, characteristic, complemented
13C22×#63218C2212yes—
14#11763364—24no—
15#11763364C2218yes—
16C2×#10587555C2211yescharacteristic
17C2×#10587556C2211yescharacteristic
18C2×#10587576C2211yescharacteristic
19C2×#10587576C2212yes—
20C2×#10587576C2211yescharacteristic
21C2×#10587575—21no—
22C2×#10587575—21no—
23#125×D17—24no—
24#125×D17C2218yes—
25C2×#10587583—21no—
26C2×#10587632—21no—
27C2×Q8×Dic17—21no—
28C2×#10587573—21no—
29C2×#10587578C2212yes—
30C2×C4⋊C4×D17—21no—
31C2×C4⋊C4×D17—21no—
32C2×C4⋊C4×D17C2211yescharacteristic
33C2×C4⋊C4×D17C2211yescharacteristic
34C2×C42×D17C2211yescharacteristic
35#11763219C2218yescomplemented
36#11763218C2218yescomplemented
37#11763215C2218yescomplemented
38#11763210C22116yescomplemented
39#11763209C22116yescomplemented
40#11762850C22116yes—
41#11762848C22116yes—
42C2×#10587489C2212yes—
43C2×#10587478C2212yes—
44C2×#10587478C2212yes—
45C2×#10587488C2212yes—
46C2×#10587479C2212yes—
47C2×#10587479C2212yes—
48#11762761C2218yes—
49C2×#10587474C2211yescharacteristic
50C2×C8×Dic17C2212yes—
51C2×C17×C4⋊Q8C2211yescharacteristic
52C2×C17×#125C2211yescharacteristic
53C17×#501C2218yescomplemented
54C2×C17×#107C2212yes—
55C2×C17×#106C2212yes—
56C2×C17×#97C2211yescharacteristic
57C22×Q8×C17—21no—
58C22×C4×D17—21no—
59C22×C4×D17—21no—
60C22×C4×D17D411yescharacteristic
61C22×C4×D17D411yescharacteristic
62C22×C4×D17C2311yescharacteristic
63C22×Dic34—21no—
64C22×C8×C17C2312yes—
65C17×C4⋊Q8—22no—
66C17×C4⋊Q8C2314yes—
67C17×#125—22no—
68C17×#125C2314yes—
69C2×C4⋊C4×C17—21no—
70C2×C4⋊C4×C17—21no—
71C2×C4⋊C4×C17—21no—
72C2×C4⋊C4×C17C2311yescharacteristic
73C2×C4⋊C4×C17C2311yescharacteristic
74C2×C4⋊C4×C17C2312yes—
75C2×C42×C17C2311yescharacteristic
76#10587632—28no—
77Q8×Dic17—28no—
78C2×#63227—22no—
79C2×C4⋊Dic17—21no—
80C2×C4⋊Dic17—21no—
81C2×C4⋊Dic17—21no—
82C2×C4⋊Dic17—22no—
83C2×C4⋊Dic17C2311yescharacteristic
84C2×C4⋊Dic17C2311yescharacteristic
85C2×C4⋊Dic17C2312yes—
86C2×#63225—21no—
87C2×#63225—21no—
88C2×#63225—21no—
89C2×#63225—21no—
90C2×#63225—21no—
91C2×#63225—21no—
92C2×#63225—22no—
93C2×C4×Dic17—22no—
94C2×C4×Dic17D411yescharacteristic
95C2×C4×Dic17D411yescharacteristic
96C2×C4×Dic17C2311yescharacteristic
97C22×#3622C2312yes—
98C2×#63218Q8116yescomplemented
99C2×#63218C2318yes—
100#10587583—28no—
101#10587578—24no—
102#10587578C2318yes—
103C4⋊C4×D17—28no—
104C4⋊C4×D17—28no—
105C4⋊C4×D17—22no—
106C4⋊C4×D17—22no—
107C4⋊C4×D17C2314yes—
108C4⋊C4×D17C2314yes—
109#10587576—22no—
110#10587576—22no—
111#10587576—24no—
112#10587576C2314yes—
113#10587576C2318yes—
114#10587576C2314yes—
115#10587575—28no—
116#10587575—28no—
117#10587573—28no—
118C42×D17D414yes—
119C42×D17C2314yes—
120#10587556—22no—
121#10587556C2314yes—
122#10587555—22no—
123#10587555C2314yes—
124C17×#107C2318yes—
125C17×#106C2318yes—
126C17×#97C2314yes—
127#10587489C2318yes—
128#10587488C2318yes—
129C8×Dic17C2318yes—
130#10587479C2318yes—
131#10587479C2318yes—
132#10587478C2318yes—
133#10587478C2318yes—
134#10587474C2314yes—
135C23×D17C2×D411yescharacteristic
136C2×Q8×C17—24no—
137C2×Q8×C17—44no—
138C22×C4×C17—21no—
139C22×C4×C17—21no—
140C22×C4×C17—22no—
141C22×C4×C17C2×D411yescharacteristic
142C22×C4×C17C2×D411yescharacteristic
143C22×C4×C17C2411yescharacteristic
144C22×Dic17—22no—
145C22×Dic17—21no—
146C22×Dic17—21no—
147C22×Dic17C2×D411yescharacteristic
148C22×Dic17C2×D411yescharacteristic
149C22×Dic17C2×D411yescharacteristic
150C2×C4×D17—24no—
151C2×C4×D17—24no—
152C2×C4×D17—42no—
153C2×C4×D17—42no—
154C2×C4×D17—44no—
155C2×C4×D17—44no—
156C2×C4×D17C2×D414yes—
157C2×C4×D17C2×D414yes—
158C2×C4×D17C2×D412yes—
159C2×C4×D17C2×Q818yes—
160C2×C4×D17C2412yes—
161C2×Dic34—24no—
162C2×Dic34—44no—
163C2×C8×C17C2×Q818yes—
164C2×C8×C17C2414yes—
165C4⋊C4×C17—21no—
166C4⋊C4×C17—21no—
167C4⋊C4×C17—24no—
168C4⋊C4×C17—24no—
169C4⋊C4×C17—22no—
170C4⋊C4×C17—24no—
171C4⋊C4×C17C2412yes—
172C4⋊C4×C17C2412yes—
173C4⋊C4×C17C2414yes—
174C42×C17C2×D412yes—
175C42×C17C2412yes—
176#63227—28no—
177C4⋊Dic17—22no—
178C4⋊Dic17—24no—
179C4⋊Dic17—21no—
180C4⋊Dic17—21no—
181C4⋊Dic17—24no—
182C4⋊Dic17—24no—
183C4⋊Dic17—28no—
184C4⋊Dic17C2412yes—
185C4⋊Dic17C2414yes—
186C4⋊Dic17C2412yes—
187#63225—24no—
188#63225—24no—
189#63225—28no—
190#63225—24no—
191#63225—24no—
192#63225—24no—
193#63225—24no—
194C4×Dic17—28no—
195C4×Dic17C2×D412yes—
196C4×Dic17C2×D414yes—
197C4×Dic17C2×D414yes—
198C4×Dic17C2412yes—
199C2×#3622C2×Q818yes—
200C2×#3622C2414yes—
201#63218C2×Q8132yescomplemented
202C2×#3166—171nomaximal, Sylow
203C23×C17C22×D411yescharacteristic
204C22×D17—22no—
205C22×D17—22no—
206C22×D17C4⋊Q814yes—
207C22×D17C22×D412yes—
208Q8×C17—48no—
209C2×C4×C17—22no—
210C2×C4×C17—22no—
211C2×C4×C17—22no—
212C2×C4×C17—22no—
213C2×C4×C17—24no—
214C2×C4×C17—42no—
215C2×C4×C17—42no—
216C2×C4×C17—44no—
217C2×C4×C17C22×D412yes—
218C2×C4×C17C22×D412yes—
219C2×C4×C17C22×D411yescharacteristic
220C2×C4×C17C22×Q814yes—
221C2×C4×C17C2511yescharacteristic
222C2×Dic17—22no—
223C2×Dic17—22no—
224C2×Dic17—24no—
225C2×Dic17—22no—
226C2×Dic17—22no—
227C2×Dic17—44no—
228C2×Dic17—42no—
229C2×Dic17—42no—
230C2×Dic17C4⋊Q814yes—
231C2×Dic17C22×D412yes—
232C2×Dic17C22×D412yes—
233C2×Dic17C22×D412yes—
234C4×D17—44no—
235C4×D17—44no—
236C4×D17—48no—
237C4×D17—48no—
238C4×D17C4⋊Q818yes—
239C4×D17C22×Q818yes—
240Dic34—48no—
241C8×C17C22×Q818yes—
242#3622C22×Q818yes—
243C2×#533—171no—
244C22×#125—171no—
245#3166—1716no—
246C2×#501—171no—
247C2×#501—171no—
248C2×#501—171no—
249C2×#501D1711yescharacteristic, complemented
250C2×#499—172no—
251C2×#499—172no—
252C2×#428—172no—
253C2×#428—172no—
254C2×C4×M16—171no—
255C22×C17C2×C4⋊Q812yes—
256C22×C17#57512yes—
257C22×C17#57512yes—
258C22×C17C23×D411yescharacteristic
259C2×D17—28no—
260C2×D17—22no—
261C2×D17—22no—
262C2×D17C2×C4⋊Q814yes—
263C4×C17—22no—
264C4×C17—22no—
265C4×C17—42no—
266C4×C17—42no—
267C4×C17—44no—
268C4×C17C2×C4⋊Q812yes—
269C4×C17C23×Q812yes—
270Dic17—22no—
271Dic17—22no—
272Dic17—44no—
273Dic17—42no—
274Dic17—42no—
275Dic17C2×C4⋊Q814yes—
276C22×M16—172no—
277#533—178no—
278#533—344no—
279C2×C4⋊Q8—171no—
280C2×C4⋊Q8C2×D1711yescharacteristic
281C2×#125—178no—
282C2×#125—171no—
283C2×#125—171no—
284C2×#125—172no—
285C2×#125—171no—
286C2×#125—341no—
287C2×#125—341no—
288C2×#125—344no—
289C2×#125C2×D1711yescharacteristic
290C2×C22⋊Q8—341no—
291C2×C22⋊Q8—341no—
292C2×C4×Q8—341no—
293C2×C4×Q8—341no—
294C2×#117—172no—
295C22×C4⋊C4—171no—
296C22×C4⋊C4—171no—
297C22×C4⋊C4—341no—
298C22×C4⋊C4—341no—
299C22×C42—171no—
300#501—178no—
301#501—178no—
302#501—178no—
303#501C2×D1718yescomplemented
304#499—1716no—
305#499—1716no—
306#428—1716no—
307#428—1716no—
308C2×#107—172no—
309C2×#107—172no—
310C2×#107—172no—
311C2×#107C2×D1712yes—
312C2×#106—172no—
313C2×#106—172no—
314C2×#106—172no—
315C2×#106C2×D1712yes—
316C4×M16—178no—
317C2×#97—171no—
318C2×#97C2×D1711yescharacteristic
319C2×C4×C8—172no—
320C2×C17#316614yescomplemented
321C2×C17C22×C4⋊Q811yescharacteristic
322C2×C17C2×#57511yescharacteristic
323C2×C17C2×#57511yescharacteristic
324D17—24no—
325C22×Q8—21no—
326C22×Q8—341no—
327C23×C4—171no—
328C23×C4—171no—
329C23×C4—171no—
330C23×C4—341no—
331C23×C4—341no—
332C2×M16—1716no—
333C2×M16—178no—
334C22×C8—172no—
335C22×C8C22×D1712yes—
336C4⋊Q8—22no—
337C4⋊Q8—174no—
338C4⋊Q8—342no—
339C4⋊Q8C22×D1714yes—
340#125—22no—
341#125—174no—
342#125—174no—
343#125—178no—
344#125—174no—
345#125—348no—
346#125—348no—
347#125—342no—
348#125—342no—
349#125—344no—
350#125—342no—
351#125C22×D1714yes—
352C22⋊Q8—348no—
353C22⋊Q8—348no—
354C4×Q8—348no—
355C4×Q8—348no—
356#117—178no—
357#117—344no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—171no—
362C2×C4⋊C4—171no—
363C2×C4⋊C4—172no—
364C2×C4⋊C4—174no—
365C2×C4⋊C4—174no—
366C2×C4⋊C4—342no—
367C2×C4⋊C4—342no—
368C2×C4⋊C4—348no—
369C2×C4⋊C4—348no—
370C2×C4⋊C4—341no—
371C2×C4⋊C4—341no—
372C2×C4⋊C4—341no—
373C2×C4⋊C4—341no—
374C2×C4⋊C4—341no—
375C2×C4⋊C4—341no—
376C2×C4⋊C4—342no—
377C2×C4⋊C4—342no—
378C2×C4⋊C4—341no—
379C2×C4⋊C4—341no—
380C2×C4⋊C4—341no—
381C2×C4⋊C4C22×D1711yescharacteristic
382C2×C4⋊C4C22×D1711yescharacteristic
383C2×C4⋊C4C22×D1712yes—
384C2×C22⋊C4—342no—
385C2×C42—171no—
386C2×C42—171no—
387C2×C42—171no—
388C2×C42—174no—
389C2×C42—174no—
390C2×C42—342no—
391C2×C42C22×D1711yescharacteristic
392#107—178no—
393#107—178no—
394#107—178no—
395#107C22×D1718yes—
396#106—178no—
397#106—178no—
398#106—178no—
399#106C22×D1718yes—
400#97—174no—
401#97C22×D1714yes—
402C4×C8—178no—
403C17C2×#316611yescharacteristic, complemented, Sylow
404C24—171no—
405C2×Q8—24no—
406C2×Q8—44no—
407C2×Q8—344no—
408C2×Q8—684no—
409C22×C4—22no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—171no—
413C22×C4—172no—
414C22×C4—178no—
415C22×C4—172no—
416C22×C4—171no—
417C22×C4—171no—
418C22×C4—174no—
419C22×C4—174no—
420C22×C4—344no—
421C22×C4—344no—
422C22×C4—342no—
423C22×C4—341no—
424C22×C4—341no—
425C22×C4—682no—
426C22×C4—682no—
427C22×C4—684no—
428C22×C4—684no—
429C22×C4D4×D1711yescharacteristic
430C22×C4D4×D1711yescharacteristic
431C22×C4C23×D1711yescharacteristic
432M16—1732no—
433C2×C8—178no—
434C2×C8—174no—
435C2×C8Q8×D1718yes—
436C2×C8C23×D1714yes—
437C4⋊C4—24no—
438C4⋊C4—24no—
439C4⋊C4—24no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—22no—
443C4⋊C4—172no—
444C4⋊C4—172no—
445C4⋊C4—174no—
446C4⋊C4—344no—
447C4⋊C4—344no—
448C4⋊C4—344no—
449C4⋊C4—344no—
450C4⋊C4—344no—
451C4⋊C4—344no—
452C4⋊C4—348no—
453C4⋊C4—348no—
454C4⋊C4—341no—
455C4⋊C4—341no—
456C4⋊C4—342no—
457C4⋊C4—344no—
458C4⋊C4—344no—
459C4⋊C4—344no—
460C4⋊C4C23×D1712yes—
461C4⋊C4C23×D1714yes—
462C4⋊C4C23×D1712yes—
463C22⋊C4—348no—
464C42—174no—
465C42—174no—
466C42—172no—
467C42—172no—
468C42—348no—
469C42D4×D1712yes—
470C42C23×D1712yes—
471C23—174no—
472C23—172no—
473C23—342no—
474C23—342no—
475C23C2×D4×D1711yescharacteristic
476Q8—48no—
477Q8—688no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—24no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—42no—
484C2×C4—44no—
485C2×C4—42no—
486C2×C4—174no—
487C2×C4—172no—
488C2×C4—178no—
489C2×C4—178no—
490C2×C4—172no—
491C2×C4—172no—
492C2×C4—342no—
493C2×C4—342no—
494C2×C4—344no—
495C2×C4—342no—
496C2×C4—342no—
497C2×C4—684no—
498C2×C4—684no—
499C2×C4—688no—
500C2×C4—688no—
501C2×C4—682no—
502C2×C4—682no—
503C2×C4—684no—
504C2×C4C2×D4×D1712yes—
505C2×C4C2×D4×D1712yes—
506C2×C4C2×D4×D1711yescharacteristic
507C2×C4C2×Q8×D1714yes—
508C2×C4C24×D1711yescharacteristic
509C8—178no—
510C8C2×Q8×D1718yes—
511C22—174no—
512C22—348no—
513C22—342no—
514C22—342no—
515C22C4⋊Q8×D1712yes—
516C22#1176360512yes—
517C22#1176360812yes—
518C22C22×D4×D1711yescharacteristic
519C4—22no—
520C4—22no—
521C4—42no—
522C4—44no—
523C4—42no—
524C4—174no—
525C4—342no—
526C4—342no—
527C4—682no—
528C4—682no—
529C4—684no—
530C4C4⋊Q8×D1712yes—
531C4C22×Q8×D1712yes—
532C2—344no—
533C2#1453933514yesdirect product factor
534C2C2×C4⋊Q8×D1711yescharacteristic
535C2C2×#1176360511yescharacteristic
536C2C2×#1176360811yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#501C2
socleC23×C17C22×D4
prime radicalC23×D17C2×D4
hypercenterC2×#501D17
hypocenterC17C2×#3166
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #14539335C2direct (N × H)
4. C2×#11763219C2semidirect
5. C2×#11763218C2semidirect
6. C2×#11763215C2semidirect
7. C2×#11763210C2semidirect
8. C2×#11763209C2semidirect
12. C2×C17×#501C2semidirect
35. #11763219C22semidirect
36. #11763218C22semidirect
37. #11763215C22semidirect
38. #11763210C22semidirect
39. #11763209C22semidirect
53. C17×#501C22semidirect
98. C2×#63218Q8semidirect
201. #63218C2×Q8semidirect
249. C2×#501D17semidirect
303. #501C2×D17semidirect
320. C2×C17#3166semidirect
403. C17C2×#3166semidirect
533. C2#14539335direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#117633642
C2×#125×D172
#145393352
C2×#117632192
C2×#117632182
C2×#117632152
C2×#117632102
C2×#117632092
C2×#117628502
C2×#117628482
C2×#117627612
C2×C17×#5012
C2×#316617